In order to see the effects of the anisotropic interaction, the
entanglement \(C_{30,31}\)  and the entanglement \(C_{25,26}\)  of the
central two qubits is plotted in Fig. 4 as a function of the time
\(t\)  for different anisotropic interaction. In Fig. 4(a), the
entanglement \(C_{30,31}\)  generates immediately after the time \(t=0\) .
The entanglement reaches the first peak rapidly and then oscillates
around a constant. The anisotropic interaction has a weak influence
on the first peak of the entanglement. The first peak decreases
slightly when the anisotropic interaction increases. When \(J_z=0.0\) ,
the entanglement oscillates around \(0.35\) . When \(J_z=0.5\) , the
entanglement oscillates around \(0.12\) . When \(J_z=1.5,2.0\) , the
entanglement oscillates around \(0.40\)  and exists all the time. For
the above cases, the entanglement maintains for a long time. While
for \(J_z=1\) , the entanglement appears and disappears alternatively.
After \(t=37\) , the entanglement disappears all the time. It is clear
that the entanglement \(C_{30, 31}\)  of the central two qubits
decreases as the anisotropic interaction \(J_z\)  increases and then
increases as \(J_z\)  increases further and finally almost saturates.
In Fig. 4(b), the entanglement \(C_{25,26}\)  generates after a short
time. This time delay is caused by the finite propagation speed of
the entanglement from the central pair to side pairs. The
entanglement reaches the first peak rapidly and then oscillates
around a constant. The anisotropic interaction has a strong
influence on the first peak of the entanglement. The height of the
first peak decreases when the anisotropic interaction increases.
When \(J_z=0\) , the first peak is \(C_{25,26}^{peak(1)}=0.427\) , while
the peak is \(C_{25,26}^{peak(1)}=0.259\)  when \(J_z=0.5\) . The
anisotropic interaction has a feeble influence on the period when
the entanglement reaches the first peak. The time of the
entanglement reaching the first peak decreases slightly when the
anisotropic interaction increases. After the entanglement reaches
the first peak, the entanglement oscillates around \(0.33\)  when
\(J_z=0.0\) . When \(J_z=0.5\) , the entanglement oscillates around
\(0.11\) . For the above cases, the entanglement exists all the time.
While for \(J_z=1\) , the entanglement appears and disappears
alternatively. After \(t=25\) , the entanglement disappears all the
time. When \(J_z=1.5, 2.0\) , the entanglement disappears and never
appears after the first peak emergences. The entanglement decreases
as the anisotropic interaction increases. It is noted that the
propagation velocity of the entanglement is slightly influenced by
the anisotropy parameter, but the damping coefficient of the
entanglement wave is strongly dependent on the anisotropic parameter[1]}, [2]}.
.
